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Chapter 33: Magnets

A rectangular grid has been filled with a mixture of magnets (that is, dominoes with one positive end and one negative end) and blank dominoes (that is, dominoes with two neutral poles). These dominoes are initially only seen in silhouette. Around the grid are placed a number of clues indicating the number of positive and negative poles contained in certain columns and rows.

Your aim is to correctly place the magnets and blank dominoes such that all the clues are satisfied, with the additional constraint that no two similar magnetic poles may be orthogonally adjacent (since they repel). Neutral poles do not repel, and can be adjacent to any other pole.

Credit for this puzzle goes to Janko [16].

Magnets was contributed to this collection by James Harvey.

[16] http://www.janko.at/Raetsel/Magnete/index.htm

33.1 Magnets controls

Left-clicking on an empty square places a magnet at that position with the positive pole on the square and the negative pole on the other half of the magnet; left-clicking again reverses the polarity, and a third click removes the magnet.

Right-clicking on an empty square places a blank domino there. Right-clicking again places two question marks on the domino, signifying ‘this cannot be blank’ (which can be useful to note deductions while solving), and right-clicking again empties the domino.

You can also use the cursor keys to move a cursor around the grid. Pressing the return key will lay a domino with a positive pole at that position; pressing again reverses the polarity and then removes the domino, as with left-clicking. Using the space bar allows placement of blank dominoes and cannot-be-blank hints, as for right-clicking.

(All the actions described in section 2.1 are also available.)

33.2 Magnets parameters

These parameters are available from the ‘Custom...’ option on the ‘Type’ menu.

Width, Height

Size of grid in squares. There will be half Width × Height dominoes in the grid: if this number is odd then one square will be blank.

(Grids with at least one odd dimension tend to be easier to solve.)

Difficulty

Controls the difficulty of the generated puzzle. At Tricky level, you are required to make more deductions about empty dominoes and row/column counts.

Strip clues

If true, some of the clues around the grid are removed at generation time, making the puzzle more difficult.